Downing Street has quashed reports of a review into Prince Andrew's trade envoy role, insisting that the prime minister has full confidence in him and the "important contribution" he has made to UK trade.

Pressure has been mounting on the prince amid claims he has become "a national embarrassment" following further revelations over the weekend about his controversial dealings with discredited business figures.

Ministers indicated that a review of the Duke of York's role as Britain's trade ambassador would be used to lower his profile.

One cabinet minister said a hard-headed assessment of Prince Andrew's role would be made during a "tasking review", which is held every six months to assess his work as Britain's special trade representative.

There were suggestions that Prince Andrew could be given more of a ceremonial role rather than his official position as trade envoy on behalf of the government body, UK Trade & Investment, while government sources indicated that they would be relieved to see the back of the prince as special trade representative.

Vince Cable, the business secretary, said on Monday morning that the prince would have to judge whether he should carry on as UK trade envoy.

But the comments appeared at odds with ones made later by David Cameron's official spokesman, who made clear that the prince has the prime minister's full support and that there will be no review of his role.

The spokesman declined to comment on unattributable briefings given over the weekend, but said the government's position was clear: "The prime minister thinks he is doing an important job and is making a major contribution and he is supportive of him in that role.

"We are not reviewing that role in any way. The government's position is very clear: that we support him in his role as trade envoy. He has made a very important contribution to UK trade through the role and continues to do so. We think he makes a valuable contribution and so does British business."

Asked whether the prime minister had full confidence in Prince Andrew as a trade envoy, the official spokesman replied: "Yes".

He refused to comment on whether there had been contact between Buckingham Palace and Downing Street on Monday, following further revelations about the prince's links with Jeffrey Epstein, a billionaire US financier who served a prison sentence for soliciting an underage girl for prostitution. The Mail on Sunday reported that the FBI is to reopen its investigation into Epstein over allegations of his involvement with underage girls.

Cable told the BBC Radio 4 Today programme that conversations would be taking place with Prince Andrew over his future role as Britain's special trade representative: "He is a volunteer, he has offered to perform these roles, and I think it is down to him essentially to judge the position he wants to be in.

"Obviously there are conversations that will take place with him about what he is to do in future. That is simply a matter of managing the relationship."

A picture was released last week of the prince with his arm around Virginia Roberts, then aged 17, who claims she was sexually exploited by Epstein and his friends. The teenager said she met the prince, who allegedly enjoyed regular massages at Epstein's home. The prince categorically denies any wrongdoing or impropriety.

Chris Bryant, a Labour MP and former foreign minister, said the royal had become "a national embarrassment" who should no longer be used as a trade ambassador.

Bryant, who was chastised by the Commons Speaker last week for raising the issue on the floor of the house, told BBC Breakfast: "I am sure there are some countries in the world where having a visiting royal makes a difference, it makes it possible to have some meetings which wouldn't otherwise be possible. But I am afraid he has now just become a national embarrassment.

"My worry is that, sometimes when he goes on these trips, I am not sure whether he is helping us out or he is just helping himself.

"The truth is we shouldn't be using him for these delegations any more."

It was reported on Monday that the prince was shortly planning to lead a trade mission to Saudi Arabia, which has been identified as one of the most attractive potential markets for British companies.

The Duke of York has held the trade role since 2001 and Downing Street cited letters from the business sector hailing the role he has played over recent years.

Though the role is unpaid, the state pays the expenses for his trip.

Mike Gapes, a member and former chairman of the House of Commons foreign affairs committee, said the prince should be replaced in the role with someone accountable to parliament.

The Labour MP for Ilford Southtold the BBC News Channel: "I'm not doubting that, over the years, he will have promoted British trade and British exports, but the argument that we have to have an unelected and unaccountable person doing that job, I think, is out of date.

"We need to recognise the revolutions taking place in the Arab world and other changes. It's now time that we actually were able to have somebody who is accountable. Because of his royal position, we in parliament are not able to hold him to account. If he was a volunteer receiving an office with financial support, we could question ministers about his role and he himself could be called before select committees of the house.

"Because of his royal position, we can't do that. We can't ask questions about the truth of the allegations that were in the newspapers and elsewhere. I think his position is untenable."